How many solutions does the system of equations below have? y = 9x + 5 y = 9x − 3/4 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze System: Analyze the given system of equations to determine the number of solutions. The system of equations is: y = 9x + 5 y = 9x - 3/4 To find the number of solutions, we need to compare the slopes and y-intercepts of the two lines represented by these equations.Identify Slopes and Y-Intercepts: Identify the slopes and y-intercepts of both equations. For the first equation, y = 9x + 5, the slope (m1) is 9 and the y-intercept (b1) is 5. For the second equation, y = 9x - 3/4, the slope (m2) is also 9 and the y-intercept (b2) is -3/4.Compare Lines: Compare the slopes and y-intercepts of the two lines. Since both lines have the same slope (m1 = m2 = 9), they are parallel to each other. However, their y-intercepts are different (b1 = 5 and b2 = -3/4). Parallel lines with different y-intercepts do not intersect and therefore have no points in common.Conclude Number of Solutions: Conclude the number of solutions based on the comparison. Because the lines are parallel and have different y-intercepts, they will never intersect. Therefore, the system of equations has no solution.

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How many solutions does the system of equations below have? $\newline$ $y = 9x + 5$ $\newline$ $y = 9x - \frac{3}{4}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Precalculus

Determine the number of solutions to a system of equations in three variables

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Q. How many solutions does the system of equations below have?

\newline

y = 9x + 5

\newline

y = 9x - \frac{3}{4}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze System: Analyze the given system of equations to determine the number of solutions. $\newline$ The system of equations is: $\newline$ $y = 9x + 5$ $\newline$ $y = 9x - \frac{3}{4}$ $\newline$ To find the number of solutions, we need to compare the slopes and $y$ -intercepts of the two lines represented by these equations.
Identify Slopes and Y-Intercepts: Identify the slopes and y-intercepts of both equations. $\newline$ For the first equation, $y = 9x + 5$ , the slope $(m_1)$ is $9$ and the y-intercept $(b_1)$ is $5$ . $\newline$ For the second equation, $y = 9x - \frac{3}{4}$ , the slope $(m_2)$ is also $9$ and the y-intercept $(b_2)$ is $-\frac{3}{4}$ .
Compare Lines: Compare the slopes and y-intercepts of the two lines. $\newline$ Since both lines have the same slope $m_1 = m_2 = 9$ , they are parallel to each other. $\newline$ However, their y-intercepts are different $b_1 = 5$ and $b_2 = -\frac{3}{4}$ . $\newline$ Parallel lines with different y-intercepts do not intersect and therefore have no points in common.
Conclude Number of Solutions: Conclude the number of solutions based on the comparison. $\newline$ Because the lines are parallel and have different $y$ -intercepts, they will never intersect. Therefore, the system of equations has $no$ solution.